Spontaneous scalarization of regular Hayward black holes in Einstein-nonlinear electromagnetic-scalar gravity

TL;DR

This work analyzes spontaneous scalarization of regular Hayward black holes within Einstein–nonlinear electrodynamics–scalar gravity. Tachyonic instability from nonminimal scalar couplings drives the formation of scalarized black holes, and the authors study two couplings, $\xi(\varphi)=1-\alpha\varphi^2$ and $\xi(\varphi)=e^{-\alpha\varphi^2}$, uncovering an infinite family of scalarized branches labeled by $n=0,1,2,...$, with the fundamental $n=0$ branch being radially stable. They construct the $n=0$ branch numerically for $M=1/2$, $q=0.25$ and show it persists for $\alpha\ge\alpha_{\mathrm{th}}(q)$, accompanied by modest modifications to the horizon and scalar hair profiles. Stability analysis of radial perturbations confirms $\Omega<0$ for the $n=0$ branch in both couplings, while higher-$n$ branches appear unstable, suggesting the $n=0$ SCBH as the end state with potential observational consequences.

Abstract

In this paper, we discuss the spontaneous scalarization of Hayward black holes in Einstein-nonlinear electromagnetic-scalar gravity. Taking into account the tachyonic instability, we obtain scalarized charged black holes (SCBHs) with quadratic (1-$α\varphi^2$) and exponential ($e^{-α\varphi^2}$) couplings, respectively. Moreover, these SCBHs can be labelled by the number of $n = 0, 1, 2,...$, where $n = 0$ is called the fundamental black hole and $n = 1, 2,...$ denote the $n$-excited black holes. We recover that the $n = 0$ branch for both couplings is stable against radial perturbations. This stability shows that this branch can be used for further observational implications.

Figures (5)

• Figure 1: Plots of potentials $V\left( {r,\alpha ,q}\right)$ with three different values $\alpha = \left\{ {{10},{\alpha }_{\text{ th }} = {39.497},{20}}\right\}$ from top to bottom near the $v$ axis. with ${\alpha }_{\mathrm{{th}}}\left( q\right) = {39.4976}\left( {0.250}\right) ,{21.1872}\left( {0.300}\right) ,12.0436\left( {0.350}\right)$.
• Figure 2: (a) Three curves of $\Omega$ in ${e}^{\Omega t}$ as a function of $\alpha$ are used to determine the thresholds of instability $\left[ {{\alpha }_{\mathrm{{th}}}\left( g\right) }\right]$ around a Hayward black hole. We find ${\alpha }_{\mathrm{{th}}}\left( q\right)= {39.4976}\left( {0.25}\right)$, ${21.1872}\left( {0.30}\right)$, $12.0436(0.35)$ when three curves cross the $\alpha$ axis. (b) Plot of radial profiles as a function of $z = r/{2M}$ for $M = {1/2}$ and $q = {0.25}$ , showing the first three static perturbed scalar solutions. The number $n$ of zero nodes describes the $n=0,1,2$ SCBHs.
• Figure 3: Plots of a SCBH solution with $q= {0.25}$ , and $M = {1/2}$ for $\alpha = {40.8134}$ (quadratic coupling) and $\alpha = {40.1819}$ (exponential coupling) in the $n = 0$ branch of $\alpha \geq {39.4976}$.
• Figure 4: Three scalar potentials ${V}_{\text{ SCBH }}$ for the $l = 0$ scalar mode around the $n = 0$ branch.
• Figure 5: The negative $\Omega$ is given as a function of $\alpha$ for the $l = 0$ scalar mode around the $n = 0$ branch, showing stability. Three dotted curves start from ${\alpha }_{n = 0} = {39.4976}$, ${21.1872}$, and ${12.0436}$. Three solid lines denote the unstable Hayward black holes [see Fig.\ref{['fig2']}].